In this paper we study the consequences of the introduction of a flat boundary on a four-dimensional (4D) covariant rank-2 gauge theory described by a linear combination of linearized gravity and covariant fracton theory. We show that this theory gives rise to a Maxwell-Chern-Simons-like theory of two rank-2 traceless symmetric tensor fields. This induced three-dimensional (3D) theory can be physically traced back to the traceless scalar charge theory of fractons, where the Chern-Simons-like term plays the role of a matter contribution. By further imposing time reversal invariance on the boundary, the Chern-Simons-like term disappears. Importantly, on the boundary of our 4D gauge theory we find a generalized U(1) Kaç-Moody algebra and the induced 3D theory is characterized by the conservation of the dipole moment.

• Received 29 May 2023
• Accepted 23 June 2023

DOI:https://doi.org/10.1103/PhysRevD.108.025009

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Published by the American Physical Society